What is (\partial)/(\partial x)(1/(xsqrt(x))) ?

The answer to (\partial)/(\partial x)(1/(xsqrt(x))) is -3/(2x^{5/2)}

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(\partial)/(\partial x)(1/(xsqrt(x)))

\frac{\partial}{\partial x} (\frac{1}{x x})

- \frac{3}{2 x ^{\frac{5}{2}}}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{x x})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{\partial}{\partial x} ((x x)^{- 1})

Apply the chain rule:

- \frac{1}{( x x ) ^{2}} \frac{\partial}{\partial x} (x x)

= - \frac{1}{( x x ) ^{2}} \frac{\partial}{\partial x} (x x)

\frac{\partial}{\partial x} (x x) = \frac{3 x}{2}

= - \frac{1}{( x x ) ^{2}} \cdot \frac{3 x}{2}

Simplify

- \frac{1}{( x x ) ^{2}} \cdot \frac{3 x}{2} : - \frac{3}{2 x ^{\frac{5}{2}}}

= - \frac{3}{2 x ^{\frac{5}{2}}}

\frac{d}{d x} (e^{x - 5} - x)

f (x) = \frac{( x ^{2} )}{( 4 + x )}

\int_{1}^{4} t^{2} ln (4 t) d t

y^{^{'}} + 6 y = t + e^{- 4 t}

\int \frac{x ^{4} + 1}{x ( x ^{2} + 1 ) ^{2}} d x

What is (\partial)/(\partial x)(1/(xsqrt(x))) ?
The answer to (\partial)/(\partial x)(1/(xsqrt(x))) is -3/(2x^{5/2)}